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Characterizations and classification of paraconvex multimaps

Mokhtar-Kharroubi Hocine

Control and Cybernetics

2022

Vol. 51, No. 3

303--325

Paraconvex multimaps are revisited in normed vector space setting. A parallel is provided with the studies conducted for real valued paraconvex functions on generalized convexities and monotonicities. Several characterizations are then obtained. The links with some generalized convexities for multimaps are examined and a first classification is achieved. In addition, two representation results for 2-paraconvex multimaps are given.

Support functions and subdifferentials

Grzybowski J., Pallaschke D., Urbański R.

Commentationes Mathematicae

2016

Vol 56, No. 1

45--53

In this paper we study Minkowski duality, i.e. the correspondence between sublinear functions and closed convex sets in the context of dual pairs of vector spaces.

On multiobjective nonlinear programming with support functions

Husain I., Ahmed A., Mattoo R. G.

Journal of Applied Analysis

2010

Vol. 16, nr 2

171-187

A multiobjective programming problem containing support functions is considered. Wolfe and Mond-Weir type vector duals to this problem are constructed and various duality results are validated under invexity and generalized invexity assumptions. Special cases are generated from these results.

Second order mixed symmetric duality in non-diferentiable multi-objective mathematical programming

Mishra S. K.

Journal of Applied Analysis

2007

Vol. 13, nr 1

117-132

A pair of Mond- Weir type second order mixed symmetric duals is presented for a class of non-differen- tiable multi-objective non-linear programming problems with multiple arguments. We establish duality theorems for the new pair of dual models under second order generalized convexity assumptions. This mixed second order dual for- mulation unifies the two existing second order symmetric dual formu- lations in the literature. Many recent works on symmetric duality are obtained as special cases of the results established in the present paper .

On the construction of set-valued measures

Siggini K. K.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 3

251-259

In [15] Topsoe characterizes the narrowly compact subsets of measures in general situations. The basie tool used is extension of a content to a measure. In this paper we generalize to tight set-valued map these theorems of extension [15, Theorem l, p. 198; Theorem 2 and 3, p. 201]. In our next papers we shall apply these results to the study of compactness in space of set-valued measures.

Limiting ellipsoid for reachability set of 2D continuous-discrete linear system with disturbances

Krasoń E.

Control and Cybernetics

1999

Vol. 28, no 2

269--279

A model of 2D continuous-discrete linear system is considered whose input disturbances are unknown but bounded by known ellipsoid. The formula for a support function of reachability set of this system is presented. A method of construction of ellipsoid limiting reachability set is proposed and illustrated with an example.